Filterbanks have been employed in many applications such as transmultiplexers, audio/image compression, and adaptive filtering. A typical perfect reconstruction filterbank is designed to filter a wide band signal comprised of a plurality of subbands or subchannels into the subbands or subchannels, process the subbands or subchannels (e.g., compress/decompress), and then recombine the subbands or subchannels into a wide band signal with an attempt to minimize distortion. Oversampled filterbanks are widely employed to reduce the computational complexity of signal processing algorithms, such as subband adaptive filtering techniques utilized in many audio/image compression techniques. After the signal channeling and signal combining algorithms are performed, the wideband signal is typically transmitted over a radio frequency (RF) wireless link to one or more other radio devices (e.g., user terminals). The transmission frequency of the RF wireless link is at a substantially higher frequency than the processing frequency of the wideband signal.
In certain situations it is desirable to reorder the subchannels or introduce subchannels from one or more independent filterbanks. For example, in satellite transmissions the transmission frequencies (e.g., downlink frequencies) are different than the receiving frequencies (e.g., uplink frequencies). Therefore, signals that are received from ground stations with subchannels over certain frequency bands are retransmitted to user terminals over different frequency bands. Additionally, in certain applications is desirable to reorder the subchannels based on transmission order which requires the channels to be reordered not only into different frequency bands but into different frequency locations. These requirements cannot be met with conventional modulated filterbanks due to aliasing distortion of the signal caused by recombining the signal into a wideband signal.
Conventional oversampled modulated filterbanks employ “aliasing cancellation” methods to remove the aliasing distortion. This works quite well as long as the subchannels are not reordered. When the subchannels are reordered, “aliasing cancellation” cannot be utilized. Furthermore, algorithms that employ alias cancellation, when combined with subchannel switching, exhibit amplitude and group delay distortion. The distortion results because, during signal re-synthesis, the adjacent subchannels can be from different sources and do not necessarily contain the information needed for aliasing cancellation.